Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators

Engineering Analysis with Boundary Elements

Volumn 33, Issue 4, 2009, Pages 514-521

  Tsai, C C ^a   Cheng, A H D ^b   Chen, C S ^c  

^a TOKO UNIVERSITY   (Taiwan)

^b The University of Mississippi   (United States)

^c University of Southern Mississippi   (United States)

Author keywords

Boundary element method; Dual reciprocity boundary element method; Method of fundamental solutions; Particular solution; Polyharmonic equation; Product of Helmholtz equation; Radial basis function; Trefftz method

Indexed keywords

ATTITUDE CONTROL; DIFFERENTIAL EQUATIONS; FEEDFORWARD NEURAL NETWORKS; HELMHOLTZ EQUATION; HOLMIUM; IMAGE SEGMENTATION; MATHEMATICAL OPERATORS; NUMERICAL METHODS; PROBABILITY DENSITY FUNCTION; PROGRAMMING THEORY; RADIAL BASIS FUNCTION NETWORKS; SPLINES;

DUAL RECIPROCITY BOUNDARY ELEMENT METHOD; METHOD OF FUNDAMENTAL SOLUTIONS; PARTICULAR SOLUTION; POLYHARMONIC EQUATION; PRODUCT OF HELMHOLTZ EQUATION; RADIAL BASIS FUNCTION; TREFFTZ METHOD;

BOUNDARY ELEMENT METHOD;

EID: 59649096448     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2008.08.007     Document Type: Article

References (32)

1. Cheng A.H.-D., and Cheng D.T. Heritage and early history of the boundary element method. Eng Anal Bound Elem 29 (2005) 268-302
2. Chen CS, Hon YC, Schaback RS. Scientific computing with radial basis functions. Submitted for publication.
3. Golberg M.A. The method of fundamental solutions for Poisson's equation. Eng Anal Bound Elem 16 (1995) 205-213
4. Li Z.C., Lu T.T., Hu H.Y., and Cheng A.H.-D. Trefftz and collocation methods (2008), WIT Press, Southampton/Boston
5. Zielinski AP. editor. First international workshop on the Trefftz method. Computer Assisted Mechanics and Engineering Science 1997;4(3/4).
6. Kansa E.J. Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics I. Comput Math Appl 19 (1990) 127-145
7. Cheng A.H.-D., Golberg M.A., Kansa E.J., and Zammito G. Exponential convergence and h-c multiquadric collocation method for partial differential equations. Numer Methods Partial Differential Equations 19 (2003) 571-594
8. Huang C.S., Lee C.-F., and Cheng A.H.-D. Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method. Eng Anal Bound Elem 31 (2007) 614-623
9. Partridge P.W., Brebbia C.A., and Wrobel L.C. The dual reciprocity boundary element method (1992), CMP/Elsevier, Amsterdam
10. Hörmander H. Linear partial differential operators (1963), Springer, Berlin
11. Atkinson K.E. The numerical evaluation of particular solutions for Poisson's equation. IMA J Numer Anal 5 (1985) 319-338
12. Cheng A.H.-D., Antes H., and Ortner N. Fundamental solutions of products of Helmholtz and polyharmonic operators. Eng Anal Bound Elem 14 (1994) 187-191
13. Cheng A.H.-D., Lafe O., and Grilli S. Dual reciprocity BEM based on global interpolation function functions. Eng Anal Bound Elem 13 (1994) 303-311
14. Cheng A.H.-D., and Morohunfola O.K. Multilayered leaky aquifer systems: I. Pumping well solution. Water Resour Res 29 (1993) 2787-2800
15. Cheng A.H.-D., and Morohunfola O.K. Multilayered leaky aquifer systems: II. Boundary element solution. Water Resour Res 29 (1993) 2801-2811
16. Cheng A.H.-D. Multilayered aquifer systems-fundamentals and applications (2000), Marcel Dekker, New York/Basel 384pp
17. O'Neil P.V. Advanced engineering mathematics (2002), International Publishing Company, London
18. Cheng A.H.-D. Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions. Eng Anal Bound Elem 24 (2000) 531-538
19. Watson G.N. A treatise on the theory of Bessel functions (1966), Cambridge University Press, Cambridge
20. Abramowitz M., and Stegun I.A. Handbook of mathematical functions (1972), Dover, New York
21. Golberg M.A., Muleshkov A.S., Chen C.S., and Cheng A.H.-D. Polynomial particular solutions for some partial differential operators. Numer Methods Partial Differential Equations 19 (2003) 112-133
22. Muleshkov A.S., Golberg M.A., and Chen C.S. Particular solutions of Helmholtz-type operators using higher order polyharmonic splines. Comp Mech 23 (1999) 411-419
23. Balaš J., Sládek V., and Sládek J. The boundary integral equation method for plates resting on a two parameter foundation. ZAMM 64 (1984) 137-146
24. Tsai C.C. The method of fundamental solutions with dual reciprocity for thin plates on Winkler foundations with arbitrary loadings. J Mech 24 (2008) 163-171
25. Golberg M.A., Chen C.S., and Karur S.R. Improved multiquadric approximation for partial differential equations. Eng Anal Bound Elem 18 (1996) 9-17
26. Cheng A.H.-D., Chen C.S., Golberg M.A., and Rashed Y.F. BEM for thermoelasticity and elasticity with body force-a revisit. Eng Anal Bound Elem 25 (2001) 377-387
27. Golberg M.A., Chen C.S., and Rashed Y.F. The annihilator method for computing particular solutions to partial differential equations. Eng Anal Bound Elem 23 (1999) 275-279
28. Janssen H.L., and Lambert H.L. Recursive construction of particular solutions to nonhomogeneous linear partial differential equations of elliptic type. J Comput Appl Math 39 (1992) 227-242
29. Karageorghis A., and Kyza I. Efficient algorithms for approximating particular solutions of elliptic equations using Chebyshev polynomials. Commun Comput Phys 2 (2007) 501-521
30. Li X., and Chen C.S. A mesh-free method using hyperinterpolation and fast Fourier transform for solving differential equation. Eng Anal Bound Elem 28 (2004) 1253-1260
31. Matthys L., Lambert H.L., and De Mey G. A recursive construction of particular solutions to a system of coupled linear partial differential equations with polynomial source term. J Comput Appl Math 69 (1996) 319-329
32. Muleshkov A.S., and Golberg M.A. Particular solutions of the multi-Helmholtz-type equation. Eng Anal Bound Elem 31 (2007) 624-630